Question: Simplify the expression. $(r^{4}+2r^{3}-3r)(6r^{3}-7r)$
Explanation: First use the distributive property. $ r^4 (6 r^3) + r^4 (-7 r) + 2 r^3 (6 r^3) + 2 r^3 (-7 r) - 3 r (6 r^3) - 3 r (-7 r) $ Simplify. $ 6r^{7} - 7r^{5} + 12r^{6} - 14r^{4} - 18r^{4} + 21r^{2} $ $6r^{7}+12r^{6}-7r^{5}-32r^{4}+21r^{2}$ Identify like terms. $ { 6r^{7}} {- 7r^{5}} {+ 12r^{6}} {- 14r^{4}} {- 18r^{4}} {+ 21r^{2}} $ Add the coefficients. $ { 6r^{7}} {+ 12r^{6}} { -7r^{5}} { -32r^{4}} {+ 21r^{2}} $